One thing I'm not following is how the side/order bias is being handled. OP measures a IMO very large bias towards left-hand treats, but it is unclear how that is handled (ahem)? Skimming https://github.com/adamwespiser/best-dog-treat/blame/main/an... doesn't help me understand if it is being modeled as a covariate to adjust for the bias or if it was dealt with by construction (eg. by always offering pairs twice, swapping hands), or what?
Incidentally OP if you want to make it more adaptive, you can just fit the B-T model each time, and grab a posterior sample of what the best pair is, and test that, which turns out to be Thompson sampling. I did this for fun with blind taste-testing of mineral waters: https://gwern.net/water